Notes on Optimal Flux Fields (2409.03426v1)

Abstract: For a given region, and specified boundary flux and density rate of an extensive property, the optimal flux field that satisfies the balance conditions is considered. The optimization criteria are the $L^{p}$-norm and a Sobolev-like norm of the flux field. Finally, the capacity of the region to accommodate various boundary fluxes and density rates is defined and analyzed.